Question

the profit that the vendor makes per day by selling x pretzels is given by the function \\(p(x) = -4x^2 + 2,800x - 200\\). find the number of pretzels that must be sold to maximize profit.

a. 1,400 pretzels
b. 350 pretzels
c. 489,800 pretzels
d. 700 pretzels

Explanation:

Identify the profit function and target

Using the Quadratic Word Problems knowledge point
The daily profit function is:

$$P(x) = -4x^2 + 2,800x - 200$$

We need to find the number of pretzels \(x\) that maximizes the profit \(P(x)\).

Find the vertex of the quadratic function

Using the Maximum Value of Quadratic knowledge point

$$
LATEXBLOCK0
$$

Answer:

• A. 1,400 pretzels
• B. 350 pretzels (Correct answer)
• C. 489,800 pretzels
• D. 700 pretzels